I understand the von Neumann entropy of a $2$-composite system is that of the reduced density matrix? What is the von Neumann entropy of an entanglement of a more than $3$ composite system?
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3$\begingroup$ sorry, I misread. Yes, the entanglement entropy is the von Neumann entropy of the reduced state. For multipartite states it's not so simple to quantify entanglement, however. See e.g. physics.stackexchange.com/a/506762/58382, quantumcomputing.stackexchange.com/a/16181/55, physics.stackexchange.com/q/184426/58382, en.wikipedia.org/wiki/Multipartite_entanglement $\endgroup$– glS ♦Commented Oct 9, 2022 at 23:58
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